We study a stochastic neural-network model in which neurons and synapses change with a priori probability p and 1–p, respectively, in the limit p0. This implies neuron activity competing with fast fluctuations of the synaptic connections—in fact, random oscillations around values given by a learning (for example, Hebb's) rule. The consequences for the system performance of a dynamics constantly checking at random the set of memorized patterns is thus studied both analytically and numerically. We describe various nonequilibrium phase transitions whose nature depends on the properties of fluctuations. We find, in particular, that under rather general conditions locally stable mixture states do not occur, and pattern recognition and retrieval processes are substantially improved for some classes of synaptic fluctuations. 相似文献
The diffusion of hard-core particles subject to a global bias is described by a nonlinear, anisotropic generalization of the diffusion equation with conserved, local noise. Using renormalization group techniques, we analyze the effect of an additional noise term, with spatially long-ranged correlations, on the long-time, long-wavelength behavior of this model. Above an upper critical dimension dLR, the long-ranged noise is always relevant. In contrast, for d<dLR, we find a weak noise regime dominated by short-range noise. As the range of the noise correlations increases, an intricate sequence of stability exchanges between different fixed points of the renormalization group occurs. Both smooth and discontinuous crossovers between the associated universality classes are observed, reflected in the scaling exponents. We discuss the necessary techniques in some detail since they are applicable to a much wider range of problems. 相似文献
In univariate Padé approximation we learn from the Froissart phenomenon that Padé approximants to perturbed Taylor series exhibit almost cancelling pole–zero combinations that are unwanted. The location of these pole–zero doublets was recently characterized for rational functions by the so‐called Froissart polynomial. In this paper the occurrence of the Froissart phenomenon is explored for the first time in a multivariate setting. Several obvious questions arise. Which definition of Padé approximant is to be used? Which multivariate rational functions should be investigated? When considering univariate projections of these functions, our analysis confirms the univariate results obtained so far in [13], under the condition that the noise is added after projection. At the same time, it is apparent from section 4 that for the unprojected multivariate Froissart polynomial no conjecture can be formulated yet.
In the last paper, the geometry of the Sz.-Nagy-Foia
model for contraction operators on Hilbert spaces was used to advantage in several problems of multivariate analysis. The lifting of intertwining operators, one of the basic results from the Sz.-Nagy-Foia
theory, is now recognized as the most adequate operatorial form of the deep classical results of the extrapolation theory. The labeling of the exact intertwining dilations given by [1]Acta Sci. Math. (Szeged) 40 9–32] and the recursive methods used there open a broad perspective for using the Sz.-Nagy-Foia
model in multivariate filtering theory. In this paper, using the notion of correlated action (see [5 and 6] Rev. Roumaine Math. Pures Appl.23, No. 9 1393–1423]) as a time domain, a linear filtering problem is formulated and its solution in terms of the coefficients of the analytic function which factorizes the spectral distribution of the known data and the coefficients of an analytic function which describes the cross correlations is given. In some special cases it is shown that the filter coefficients can be determined using recursive methods from the intertwining dilation theory, of the autocorrelation function of the known data and an intertwining operator, interpreted as the initial estimator given by the prior statistics. 相似文献
It is shown that unlike nondegenerate (linear) diffusion processes, nonlinear diffusion processes can have a periodic law. We provide an example of a nonlinear diffusion for which periodic behavior is even created by the noise, i.e. no periodicity occurs when the noise is turned off. In the second part of the paper we give an example of a one-dimensional nonlinear diffusion which can be stabilized by noise. Finally we show also that the N-dimensional (N ≥ 2) ‘linear’ diffusion approximations of that system are stabilized by noise. 相似文献
We study the semidiscrete Galerkin approximation of a stochastic parabolic partial differential equation forced by an additive space-time noise. The discretization in space is done by a piecewise linear finite element method. The space-time noise is approximated by using the generalized L2 projection operator. Optimal strong convergence error estimates in the L2 and
norms with respect to the spatial variable are obtained. The proof is based on appropriate nonsmooth data error estimates for the corresponding deterministic parabolic problem. The error estimates are applicable in the multi-dimensional case.
AMS subject classification (2000) 65M, 60H15, 65C30, 65M65.Received April 2004. Revised September 2004. Communicated by Anders Szepessy. 相似文献
In this paper we explicitly solve a non-linear filtering problem
with mixed observations, modelled by a Brownian motion and a generalized Cox
process, whose jump intensity is given in terms of a Lévy measure.
Motivated by empirical observations of R. Cont and P. Tankov we propose a
model for financial assets, which captures the phenomenon of
time inhomogeneity of the jump size density. We apply the explicit formula
to obtain the optimal filter for the corresponding filtering problem. 相似文献
In this paper we give an account of a new change of perspective in non-linear modelling and prediction as applied to smooth systems. The core element of these developments is the Gamma test a non-linear modelling and analysis tool which allows us to examine the nature of a hypothetical input/output relationship in a numerical data-set. In essence, the Gamma test allows us to efficiently calculate that part of the variance of the output which cannot be accounted for by the existence of any smooth model based on the inputs, even though this model be unknown. A key aspect of this tool is its speed: the Gamma test has time complexity O(
), where M is the number of data-points. For data-sets consisting of a few thousand points and a reasonable number of attributes, a single run of the Gamma test typically takes a few seconds. Around this essentially simple procedure a new set of analytical tools has evolved which allow us to model smooth non-linear systems directly from the data with a precision and confidence that hitherto was inaccessible. In this paper we briefly describe the Gamma test, its benefits in model identification and model building, and then in more detail explain and motivate the procedures which facilitate a Gamma analysis. We briefly report on a case study applying these ideas to the practical problem of predicting level and flow rates in the Thames valley river basin. Finally we speculate on the future development and enhancement of these techniques into areas such as datamining and the production of complex non-linear models directly from data via graphical representations of process charts and automated Gamma analysis of each input-output node. 相似文献